Abstract
This paper explains the Unimodular gauge fixing of gravity and supergravity in the framework of a perturbative BRST construction. The unphysical sector contains additional BRST-exact quartets to suppress possible ambiguities and impose both the Unimodular gauge fixing condition on the metric and a gauge condition for the reparametrization symmetry of the unimodular part of the metric. The Unimodular gauge choice of the metric must be completed by a γ-Traceless gauge condition for the Rarita–Schwinger field in the case of supergravity. This gives an interesting new class of gauges for gravity and supergravity.
Highlights
Albert Einstein recognized as early as in 1916 that there is a preferred gauge in classical gravity
The scalar bosonic fields L, b and fermionic fields η, η count altogether for zero=1+1-1-1 degrees of freedoms in unitary relations provided their dynamics is governed by an s-exact action defining invertible propagators. Having available this extra set of unphysical fields is exactly what one needs to get a Lagrangian with invertible propagators in the Unimodular gauge, with a BRST invariant gauge fixing of zero modes that otherwise would spoil the definition of gravity by a path integral in the Unimodular gauge
The fields b and λ have been eliminated by their algebraic equations of motion. This BRST invariant action depends on the metric and on the Rarita–Schwinger field only through their unimodular and γ-Traceless components gμν and Ψμ
Summary
Albert Einstein recognized as early as in 1916 that there is a preferred gauge in classical gravity. This paper is aimed at building a local quantum Lagrangian that defines gravity and supergravity unambiguously in the Unimodular gauge, at least for defining a consistent perturbative BRST invariant quantum field theory. For any given choice of a classical gauge function, getting a BRST symmetry invariant gauge fixing is necessary to possibly enforce all relevant Ward identities that define the quantum theory eventually. Having a well-defined perturbative quantization of gravity in the unimodular gauge makes contact with the work of York [13], who showed that what the classical Einstein equations truly propagate are the equivalence classes of metrics defined modulo Weyl transformations. The expression of observables may occur with more complicated expressions
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